Suppose two firms face market demand of P=150-Q, where Q = q1+ q2. Both firms have the same unit cost of C, C=28. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. a) What is the follower's total revenue function? b) Determine the equilibrium output level for both the leader and the follower. c) Determine the equilibrium market price. d) Determine the profits of the leader and the follower.
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- Suppose two firms face market demand of P=150-Q, where Q = q1+q2. Both firms have the same unit cost of C, C=28. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. a) What is the follower's total revenue function? b) Determine the equilibrium output level for both the leader and the follower. c) Determine the equilibrium market price, the profits of the leader and the follower. Note: The writing is clear and abbreviations are not allowed.Suppose two firms face market demand of P=150-Q, where q=q1+q2 . Both firms have the same unit cost of C=20. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. a) What is the follower’s total revenue function? b) Determine the equilibrium output level for both the leader and the follower. c) Determine the equilibrium market price. d) Determine the profits of the leader and the follower.Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. 1.What is the follower’s total revenue function? 2.Determine the equilibrium output level for both the leader and the follower. 3.Determine the equilibrium market price. 4.Determine the profits of the leader and the follower.
- Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.Suppose two firms face market demand of P=150-Q, where Q=q1+q2. Both firms have the same unit cost of 22. Assume the firms compete a la Firm 1 is the leader and Firm 2 is the follower in this market. 1.What is the follower’s total revenue function? 2.Determine the equilibrium output level for both the leader and the follower. 3.Determine the profits of the leader and the follower.
- 2. A homogenous good industry consists of two firms (firm 1 and firm 2). Their cost functions are cq and cq2, respectively, where c<2. The market demand function is p=10-Q, where Q=q₁+q₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' choices in the Bertrand-Nash equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' choices in the Cournot-Nash equilibrium. (c) Assume the two firms play the Stackelberg game with firm 1 as the leader. Find the firms' equilibrium choices in the Stackelberg equilibrium.There are two firms that are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q₁+q2. Each firm's marginal cost is constant at 12, and fixed cost are 0. Answer the following question, assuming that the firms are Cournot competitors. a. Calculate each firm's reaction function and illustrate them graphically (15 points) b. How much output does each firm produce? (12.5 points) c. What is the market price? (7.5 points) d. How much profit does each firm earn? What is the industry profit? (10 points)Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.
- The inverse market demand curve is P = 170-40. Two firms in this market evenly split the output. Each firm produces its product at a constant marginal cost of $10. Which of the following statements is/are TRUE? I. If one firm produces 2 more units of output, its profits will rise to $864. II. If neither firm cheats, each firm will earn a profit of $800. III. If one firm produces 3 more units of output, the other firm's profits will fall to $680. I and II I and III II and III I, II, and IIITwo Cournot competitors face inverse demand p = 50-Q, where Q = 9₁ +92 is the total output of firms 1 and 2. Both firms have marginal cost of 2. What are the equilibrium output levels q₁ and 92? 16 and 16 25 and 25 20 and 9 36 and 31. Consider a market with three firms (i = 1, 2, 3), which have identical marginal costs C = c2 = C3 = 0. The inverse demand function is given by p = 1- Q, where Q = q1 + 92 + q3. a. Compute the Cournot equilibrium, i.e., the market price and quantity. b. Assume that two of the three firms merge. Show that the profit of merging firms decreases. c. What happens to the market price if all three firms merge compared to part (a)?